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Open Access Green as soon as Postprint is submitted to ZB.
Surface spline approximation on SO(3).
Appl. Comput. Harmon. Anal. 31, 169-184 (2011)
The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of Green's functions of certain differential operators on the rotation group. They are conditionally positive definite and have a simple, closed-form expression, lending themselves to direct implementation via, e.g., interpolation or least-squares approximation. To gauge the approximation power of the underlying spaces, we introduce an approximation scheme providing precise Lp error estimates for linear schemes, namely with Lp approximation order conforming to the Lp smoothness of the target function.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Rotation group; Wigner D-function; Lie group; Lebesgue constant; Positive definite kernel; Surface spline; Polyharmonic kernel
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Quellenangaben
Volume: 31,
Issue: 2,
Pages: 169-184
Publisher
Academic Press
Publishing Place
San Diego, Calif. [u.a.]
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)